There is an extensive literature concerned with the analysis of changing images and with the characterization of motion within images. Much of this work is based on the concept of optical flow. This allows the continuity equation of fluid dynamics to be applied directly to image processing problems. Thus much of the extensive corpus of knowledge dealing with the manipulation of the partial differential equations used in fluid dynamics can be brought to bear on image processing problems.
This approach has some serious shortcomings. The underlying assumptions that the domain of investigation, in this case the image intensity function, is everywhere continuous and differentiable is rarely true in practice. The image intensity function is usually a function on a discrete domain of subscript values not on a continuum and rapid changes in intensity called “edges” are common in most images of interest. Such rapid changes in intensity preclude the use of Taylor's theorem in establishing the underlying equations of the optical flow method. The practical consequence of this is that optical flow methods have not proven to be particularly successful in the processing of images. This is hardly surprising when one considers that the very features that facilitate the alignment of images at an intuitive level, that is, sharp edges, have been sacrificed at the outset.
Another approach is to divide the image domain into zones and detect the presence or absence of intensity differences within each zone. This method is limited by the coarseness of this subdivision, which decreases the spatial resolution, and by its inability to independently track two different objects when they pass one another.
Further, changes in pixel intensity can also be brought about by causes other than objects moving in the scene. In particular changes in scene illumination will cause significant changes in image pixel intensity. These intensity changes are then passed to downstream algorithms and give rise to spurious “moving objects” or false alarms. To some extent brightness compensating cameras ameliorate the problem but they cannot compensate for brightness changes that vary across the image.